Weight reduction in the transportation is the most effective way for reducing fuel consumption. Carbon fiber composites have been increasingly used by automotive manufacturers in vehicle nonstructural and structural parts. Larger penetration of carbon fiber-based materials requires very large quantities of fiber at a low price, and of consistently high quality. The advancements in carbon fiber technology that are required to achieve this production scale-up and cost reduction, are very challenging. The most expensive production step is the conversion of textile-grade polyacrylonitrile (PAN) precursor to carbon fiber. The conversion takes place in three main stages: stabilization, low and high temperature carbonization. Most of the research to date has focused on the stabilization of the PAN precursors and oxidized PAN fibers. Comparingly little effort has been dedicated to the investigation of processing conditions during low temperature (LT) carbonization. During this stage of fiber conversion, the largest fiber mass loss occurs, and the fundamental carbon fiber structure and material properties are established. The understanding of the conversion processes in the LT furnace, and the effects of spatial and temporal variations of the LT process parameters on the carbon fiber properties are necessary to identify possible process improvements and cost savings. The objective of this research was to develop computational models for gas flow and energy transport in the gas and fiber phases of the LT furnace, and to couple them with the fiber conversion process models. The model is implemented in the three-dimensional framework that enables analysis of process condition variations in all directions. The formulation is based on modified transport equation to simulate steady state conditions and thus significantly reduce computational effort associated with transient methods. The model is implemented in open source computational fluid dynamics (CFD) code OpenFOAM. The model has been demonstrated on a prototype carbon fiber LT furnace and can be extended to other geometries and process conditions. Extensions to other physical effects, such as accounting evolution of multiple gas species, and fiber tensioning are straightforward. The model uses High Performance Computing (HPC) capabilities of OpenFOAM and can be implemented on multi-processor workstations or mid-size computer clusters common in the industrial setting.